{
  "id": 3109,
  "curve_key": "4368:-285120",
  "ainvs": [
    "0",
    "0",
    "0",
    "-91",
    "330"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2,
    2
  ],
  "naive_height": 25.14618155227422,
  "faltings_height": -0.030062530661370827,
  "conductor": "272",
  "bad_primes": [
    "2",
    "17"
  ],
  "discriminant": "1183744",
  "regulator": "1.018148717345369171061052374517851191729",
  "points": [
    [
      "7",
      "6"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 272b2 = LMFDB 272.b2: https://www.lmfdb.org/EllipticCurve/Q/272/b/2\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 272, minimal discriminant 1183744, torsion ℤ/2ℤ × ℤ/2ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:37:43",
  "updated_at": "2026-09-26 20:37:43"
}